Given an isosceles trapezoid. Prove $$A=\frac{a+b}{2},\qquad G=\sqrt{ab},\qquad H=\left(\frac{\frac1a+\frac1b}{2}\right)^{-1}$$ and $$\min\{a,b\}\le H\le G\le A\le\max\{a,b\}$$